项目名称: 有限差分多尺度计算研究
项目编号: No.11272009
项目类型: 面上项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 唐少强
作者单位: 北京大学
项目金额: 78万元
中文摘要: 多尺度计算在微纳尺度科学中有着重要应用价值,准确高效的数值方法、特别是数值界面处理方法是实现高置信度多尺度计算的基础。本项目拟在我们提出的有限差分多尺度框架、匹配界面条件和双向界面条件基础上,深入研究晶状固体多尺度计算方法,着重采用波动观点,设计一维和高维晶体多尺度计算中原子界面准确加载方案及热浴方案,研制更加准确高效的匹配核函数界面条件,并将已建立的数值界面处理方法推广到量子力学薛定谔方程中,实现多数值尺度耦合计算。本研究将为晶状固体应用问题的准确高效多尺度计算提供坚实的技术支持。
中文关键词: 多尺度;边界条件;有限温度原子模拟;薛定谔方程;分数阶导数
英文摘要: Multiscale simulations have fundamental value in micro and nano sciences. Accurate and efficient algorithms and interfacial treatments serve as the basis for high-confidence multiscale computations. In this study, we propose to investigate multiscale simulation methods for crystalline solids, based on our previous work of finite difference multiscale approach, matching boundary conditions and two-way interfacial conditions. Taking a view of wave propagation, we shall focus on the accurate loading strategy for atomic interface in a multiscale computation, and thermal-bath loading for one and multiple dimensional crystalline solids; and the design of more accurate and effective matching time history kernel interfacial conditions. We plan to further extend the boundary treatments to the Schrodinger equation in quantum mechanics. We shall realize the coupled computations with multiple numerical scales. This research will provide a sound basis for accurate and effective multiscale simulations for application problems in crystalline solids.
英文关键词: multiscale;boundary condition;finite temperature atomic simulation;Schrodinger equation;fractional derivative